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This book introduces readers to copula-based statistical methods
for analyzing survival data involving dependent censoring.
Primarily focusing on likelihood-based methods performed under
copula models, it is the first book solely devoted to the problem
of dependent censoring. The book demonstrates the advantages of the
copula-based methods in the context of medical research, especially
with regard to cancer patients' survival data. Needless to say, the
statistical methods presented here can also be applied to many
other branches of science, especially in reliability, where
survival analysis plays an important role. The book can be used as
a textbook for graduate coursework or a short course aimed at
(bio-) statisticians. To deepen readers' understanding of
copula-based approaches, the book provides an accessible
introduction to basic survival analysis and explains the
mathematical foundations of copula-based survival models.
This book provides statistical methodologies for time series data,
focusing on copula-based Markov chain models for serially
correlated time series. It also includes data examples from
economics, engineering, finance, sport and other disciplines to
illustrate the methods presented. An accessible textbook for
students in the fields of economics, management, mathematics,
statistics, and related fields wanting to gain insights into the
statistical analysis of time series data using copulas, the book
also features stand-alone chapters to appeal to researchers. As the
subtitle suggests, the book highlights parametric models based on
normal distribution, t-distribution, normal mixture distribution,
Poisson distribution, and others. Presenting likelihood-based
methods as the main statistical tools for fitting the models, the
book details the development of computing techniques to find the
maximum likelihood estimator. It also addresses statistical process
control, as well as Bayesian and regression methods. Lastly, to
help readers analyze their data, it provides computer codes (R
codes) for most of the statistical methods.
This book introduces readers to statistical methodologies used to
analyze doubly truncated data. The first book exclusively dedicated
to the topic, it provides likelihood-based methods, Bayesian
methods, non-parametric methods, and linear regression methods.
These procedures can be used to effectively analyze continuous
data, especially survival data arising in biostatistics and
economics. Because truncation is a phenomenon that is often
encountered in non-experimental studies, the methods presented here
can be applied to many branches of science. The book provides R
codes for most of the statistical methods, to help readers analyze
their data. Given its scope, the book is ideally suited as a
textbook for students of statistics, mathematics, econometrics, and
other fields.
This book introduces readers to advanced statistical methods for
analyzing survival data involving correlated endpoints. In
particular, it describes statistical methods for applying Cox
regression to two correlated endpoints by accounting for dependence
between the endpoints with the aid of copulas. The practical
advantages of employing copula-based models in medical research are
explained on the basis of case studies. In addition, the book
focuses on clustered survival data, especially data arising from
meta-analysis and multicenter analysis. Consequently, the
statistical approaches presented here employ a frailty term for
heterogeneity modeling. This brings the joint frailty-copula model,
which incorporates a frailty term and a copula, into a statistical
model. The book also discusses advanced techniques for dealing with
high-dimensional gene expressions and developing personalized
dynamic prediction tools under the joint frailty-copula model. To
help readers apply the statistical methods to real-world data, the
book provides case studies using the authors' original R software
package (freely available in CRAN). The emphasis is on clinical
survival data, involving time-to-tumor progression and overall
survival, collected on cancer patients. Hence, the book offers an
essential reference guide for medical statisticians and provides
researchers with advanced, innovative statistical tools. The book
also provides a concise introduction to basic multivariate survival
models.
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